If $x \otimes y = x^{2}-2y^{2}$ and $x \bigtriangledown y = x+5y$, find $(2 \otimes -4) \bigtriangledown 4$.
Solution: First, find $2 \otimes -4$ $ 2 \otimes -4 = 2^{2}-2(-4)^{2}$ $ \hphantom{2 \otimes -4} = -28$ Now, find $-28 \bigtriangledown 4$ $ -28 \bigtriangledown 4 = -28+(5)(4)$ $ \hphantom{-28 \bigtriangledown 4} = -8$.